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Simplifying 9(v + 1) = 2(3v + 1) + -8 Reorder the terms: 9(1 + v) = 2(3v + 1) + -8 (1 * 9 + v * 9) = 2(3v + 1) + -8 (9 + 9v) = 2(3v + 1) + -8 Reorder the terms: 9 + 9v = 2(1 + 3v) + -8 9 + 9v = (1 * 2 + 3v * 2) + -8 9 + 9v = (2 + 6v) + -8 Reorder the terms: 9 + 9v = 2 + -8 + 6v Combine like terms: 2 + -8 = -6 9 + 9v = -6 + 6v Solving 9 + 9v = -6 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. 9 + 9v + -6v = -6 + 6v + -6v Combine like terms: 9v + -6v = 3v 9 + 3v = -6 + 6v + -6v Combine like terms: 6v + -6v = 0 9 + 3v = -6 + 0 9 + 3v = -6 Add '-9' to each side of the equation. 9 + -9 + 3v = -6 + -9 Combine like terms: 9 + -9 = 0 0 + 3v = -6 + -9 3v = -6 + -9 Combine like terms: -6 + -9 = -15 3v = -15 Divide each side by '3'. v = -5 Simplifying v = -5
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